PSI - Issue 44

Gianfranco De Matteis et al. / Procedia Structural Integrity 44 (2023) 681–688 Gianfranco De Matteis et al. / Structural Integrity Procedia 00 (2022) 000–000

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3.3. Nonlinear analysis The nonlinear analysis was performed in Abaqus software. The numerical model included all the structural elements composing a single span of the deck of the investigated bridge (i.e., longitudinal and transversal beams and slab). The model was assembled with 8-node solid elements with reduced integration (C3D8R) for the concrete material, and truss elements for the steel rebars (T3D2). The mesh size was defined in order to guarantee a number of elements equal to 8 along the height of the main longitudinal beams of the models. A perfect adhesion was considered between steel and concrete and thus an embedded constraint was introduced, while the external boundaries were defined to reproduce the simply supported conditions of the investigated deck portion. The concrete behaviour was simulated through the Concrete Damage Plasticity (CDP) material model by assuming a parabolic compressive uniaxial law and a tensile strength according to EC2 (EN 1992-2, 2004). The post elastic tensile behaviour was defined with a linear softening in terms of Fracture Energy, whose value was set according to Model Code 2010 (fib, 2012). Neither compressive nor tensile damage laws were considered for the performed simulation. For the other parameters, conventional values were adopted; in detail, i. uniaxial-to-biaxial compressive strength ratio f c0 / f b0 = 1.16; ii. dilation angle ψ = 35°; iii. Kc = 0.667; iv. eccentricity ε = 0.1. As for the steel behaviour, a plastic material model having the uniaxial constitutive relationship suggested by EC2 was adopted to simulate the post-elastic response of the rebars. Both concrete and steel material strengths were defined according to the methodology described in Section 1. The load combination maximizing the positive bending moment was considered (LC1), since it returned the minimum safety factor according to the linear analysis methodologies. A force-controlled static analysis was performed, in which each load was linearly incremented according to the following load paths: • attainment of the characteristic values of the loads; • attainment of the combination values of the loads; • linear increments of the combination values of the loads. The ultimate failure load was considered reached when the model was no longer able to withstand any load increment, including the cases in which numerical convergence was not reached. The safety check was thus performed according to Eq. (1a). The modelling strategy described above was previously validated against results from the literature, according to the methodology outlined in Section 2.2. In particular, tests referring respectively to beams under simple bending (Mathey & Watstein, 1960) and under shear (Karayannis & Chalioris, 2013) were considered in the calibration. The results provided a value ~ γ Rd =1.05 and thus the modelling strategy was accepted. Nonetheless, in the calculation γ Rd =1.06 thus, γ O =1.27, was assumed. The nonlinear analysis of the deck bridge provided a capacity in terms of multiplier of the combination load equal to = 1.28 (obtained for a vertical displacement of about 50 mm), i.e., the safety check is satisfied. At the end of the analysis, both concrete and steel elements of the slab were in the elastic field, demonstrating the sufficient capacity of the deck slab against the considered load combination. Conversely, wide concrete regions experiencing plastic strains, with simultaneous yielding of bottom longitudinal steel bars, were observed in the longitudinal beams, typical of a flexural failure. In Fig. 4, the combination load multiplier-displacement curve together with the plastic tensile strain of the concrete and equivalent (Von Mises) plastic strains of the steel bars obtained at the end of the analysis are shown. In particular, the displacements are computed in the node that exhibited the maximum vertical displacement of the whole model (i.e. the midspan of the second longitudinal beam). 4. Conclusions In this paper, the application of NLA for the assessment of existing reinforced concrete bridges is investigated. Major issues are identified and relevant suggestions are proposed with respect to (i) the definition of material strengths, (ii) the assessment of model uncertainty and acceptance criteria for the solution strategy, and (iii) the opportunity of nonlinear analyses compared to linear approaches based on refined geometrical modelling of the bridge. Suggestions provided in this study are then applied to a case study constituted by a two-span reinforced concrete bridge. The bridge is analysed through conventional and non-conventional (i.e., based on refined geometrical